Generalized microkinetic model

The microkinetic models in this section are built upon BEP-relations of the type described above. It will be shown that an underlying BEP-relation in general leads to the existence of a volcano relation. We shall also use the microkinetic models in combination with the universal BEP-relation to explain why good catalysts for a long range of reactions lie in a surprisingly narrow interval of dissociative chemisorption energies. 

In Eq (4) S/So and Serelative surface area and relative equilibrium surface area, respectively, ks is the sintering rate constant. Seq/So = 0.018 and ks=1.81 1/hr are estimated from the calculated changes in relative surface area by the microkinetic model (Fig. 3D). Although the data fitted well the typical sintering kinetic model of general power law, the possible effect of encapsulating carbon deposition on the decrease in the surface area can not simply be excluded. 

Similar microkinetic models developed by other groups [37-39] revealed similar close agreement between the experimental data from single crystal studies and "real" catalysis, and at a symposium in honor of H. Topsoe and A. Nielsen, two of the leaders in industrial ammonia synthesis, general agreement was reached that the main aspects of catalytic ammonia synthesis are now essentially understood [40]. 

In general, a mechanism for any complex reaction (catalytic or non-catalytic) is defined as a sequence of elementary steps involved in the overall transformation. To determine these steps and especially to find their kinetic parameters is very rare if at all possible. It requires sophisticated spectroscopic methods and/or computational tools. Therefore, a common way to construct a microkinetic model describing the overall transformation rate is to assume a simplified reaction mechanism that is based on experimental findings. Once the model is chosen, a rate expression can be obtained and fitted to the kinetics observed. 

Instationary kinetic methods are an important experimental tool for microkinetic modeling. In the present paper theoretical and experimental approaches of instationary kinetics will be considered. After some general discussions, experimental devices will be described, followed by the presentation of selected results. 

For the microkinetic modeling of Pt-Sn/catalyst, there is a question about which DFT results should be used, Pt(lll), Pt(211), or Pt-Sn alloy. It was generally accepted that Pt was the active sites for DHP reaction on supported Pt-Sn catalyst, while Sn existed in oxide state. But, some recent works reported that Pt-Sn alloys stiU have fairly high activity (Iglesias-Juez et al., 2010 Vu et al., 2011a), which shows that the real nature of Pt-Sn catalyst is comphcated and still a matter of debate. The Pt-Sn structure properties depend on several factors, such as the nature of support, method of catalyst preparation, metaUic precursor, sequence of preparation, etc. (Resasco, 2002 Sanfihppo and Miracca, 2006). 

With eqns (1.52) and (1.53) there are four equations for the four unknown coverages 0q2> o, dco, and 0 and the system of nonlinear algebraic equations may be solved numerically. With currently available CPU speeds numerical solutions to microkinetic models for catalyst screening studies are generally preferred because they avoid the need to make any additional assumptions regarding the mechanism. 

As discussed in Section 1.6.1 the microkinetic model may be solved as a system of ODEs or non-linear algebraic equations using the steady-state assumption. It turns out that, regardless of which approach you want to use, the function that must be passed to an ODE solver or numerical root-finding method is the same Here, the more general case of the ODE system is chosen. Note that we named the previously defined function get ratesQ. 

In the kinetic modelling of catalytic reactions, one typically takes into account the presence of many different surface species and many reaction steps. Their relative importance will depend on reaction conditions (conversion, temperature, pressure, etc.) and as a result, it is generally desirable to introduce complete kinetic fundamental descriptions using, for example, the microkinetic treatment [1]. In many cases, such models can be based on detailed molecular information about the elementary steps obtained from, for example, surface science or in situ studies. Such kinetic models may be used as an important tool in catalyst and process development. In recent years, this field has attracted much attention and, for example, we have in our laboratories found the microkinetic treatment very useful for modelling such reactions as ammonia synthesis [2-4], water gas shift and methanol synthesis [5,6,7,8], methane decomposition [9], CO methanation [10,11], and SCR deNO [12,13]. 

For the simulation of RD columns in which the chemical reactions take place at heterogeneous catalysts, it is important to keep in mind that a macrokinetic expression (5.55) has to be applied. Therefore, the microkinetic rate has to be combined with the mass transport processes inside the catalyst particles. For this purpose a model for the multicomponent diffusive transport has to be formulated and combined with the microkinetics based on the component mass balances. This has been done by several authors [50-53] by use of the generalized Maxwell-Stefan equations. 

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